Yodel: A Yield Stress Model for Suspensions

Abstract

A model for the yield stress of particulate suspensions is presented that incorporates microstructural parameters taking into account volume fraction of solids, particle size, particle size distribution, maximum packing, percolation threshold, and interparticle forces. The model relates the interparticle forces between particles of dissimilar size and the statistical distribution of particle pairs expected for measured or log‐normal size distributions. The model is tested on published data of sub‐micron ceramic suspensions and represents the measured data very well, over a wide range of volume fractions of solids. The model shows the variation of the yield stress of particulate suspensions to be inversely proportional to the particle diameter. Not all the parameters in the model could be directly evaluated; thus, two were used as adjustable variables: the maximum packing fraction and the minimum interparticle separation distance. The values for these two adjustable variables provided by the model are in good agreement with separate determinations of these parameters. This indicates that the model and the approximations used in its derivation capture the main parameters that influence the yield stress of particulate suspensions and should help us to better predict changes in the rheological properties of complex suspensions. The model predicts the variation of the yield stress of particulate suspensions to be inversely proportional to the particle diameter, but the experimental results do not show a clear dependence on diameter. This result is consistent with previous evaluations, which have shown significant variations in this dependence, and the reasons behind the yield stress dependence on particle size are discussed in the context of the radius of curvature of particles at contact.